The values of x are 1/ 5 and 11 respectively.
What are algebraic expressions?Algebraic expressions are expressions that are comprised of terms, constants, coefficients, variables and factors.
They are also made up of arithmetic operations made up of subtraction, addition, multiplication, division.
To determine the expressions, we have;
1. Let the number be x
We have the expression as;
6x - 8 = x - 7
collect like terms
6x - x = - 7 + 8
5x = 1
Make 'x' the subject
x = 1/ 5
2. Let the number be x
2x = x + 11
collect like terms
2x - x = 11
x = 11
Thus, the values of x are 1/ 5 and 11 respectively.
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A boat is traveling at a constant rate through the water. if it takes 15 minutes to travel 2.7 miles, how many hours will it take for the boat to finish a 17.1 mile journey?
Answer:
6.3 hours
Step-by-step explanation:
Consider the following:
X 31 51 87 102 120
Y 206 229 184 126 103
1) What is slope of the regression line predicting Y from X,rounded to 2 decimal places?
Type numbers in the boxes.
Part 1: 10 points
Part 2: 10 points
Part 3: 10 points
3) What is the correlation between X and Y, rounded to 2 decimal places?
30 points
2) What is the intercept of the regression line predicting Y from X, rounded to 2 decimal places?
From the regression line of the data, we have that:
1) The slope is of -1.31.
2) The intercept is of 272.17.
3) The correlation coefficient is of -0.9.
How to find the equation of linear regression using a calculator?To find the equation, we need to insert the points (x,y) in the calculator.
For this problem, the points are given as follows:
(31, 206), (51, 229), (87, 184), (102, 126), (120, 103).
Inserting these points into a calculator, the equation of the line is:
y = -1.31x + 272.17.
Hence:
1) The slope is of -1.31.
2) The intercept is of 272.17.
Also inserting these points into a calculator, the correlation coefficient is of -0.9.
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Dana bought 1.8 ounces of flour and she used 0.81 ounces of it to make biscuits. How much is left?
2. Select the numerical representation for the description.
Twenty-seven percent of three million:.
O27 x 3,000,000
O 0.27 x 3,000,000
O 0.27-3,000,000
O 0.27 +3,000,000
0.27 3,000,000
Answer:
27% of a 3m is 810,000
but here answer r is 0.27 3,000,000
Numerical representation of Twenty-seven percent of three million will be 0.27 x 3,000,000 .
The correct option is B.
Given, word form Twenty-seven percent of three million.
Conversion of word form into numerical form.
1 million = 1,000,000
Using unitary method,
Multiply both sides by 3.
1 million × 3 = 1,000,000 × 3
3 million = 3,000,000
Now 27% in terms of fraction can be written as :
27% = [tex]\frac{27}{100}[/tex]
= 0.27
Combining ''Twenty-seven percent of three million" :
Of in mathematics represent multiplication .
0.27 × 3000000
Thus the correct option is B .
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what is 4 multiplied by 4
Answer:
4 × 4 is 16.
Multiplication:
Multiplication is the operation of increasing a value by another value the number of times the other value says to increase the first value.
e.g, 5 × 6 = 30
determine whether the statement describes a descriptive or inferential statistic. a survey of 1455 people revealed that 53% work a full-time job; therefore it can be assumed that 53% of the u.s. population works a full-time job.
The statement, "A survey of 1455 people revealed that 53% work a full-time job; therefore it can be assumed that 53% of the u.s. population works a full-time job" describes Inferential statistics.
What is inferential statistics?Inferential statistics is a sort of statistic that requires people to reach a conclusion based on some previously provided samples. In the statement above, we can see some statistics that have been previously stated that is followed by a conclusion.
The assumption that is made in the latter part of the statement is the reason why the statement can be referred to as inferential statistics.
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Factor.
y²-9 please help me with this
Since both terms are perfect squares, factor using the difference of squares formula,
a2−b2=(a+b)(a−b) where a=y and b=3.
(y+3)(y−3)
all employees surveyed said that if they were in a state of information underload, they were dissatisfied.
Nearly 80% of those surveyed said they want to work for a company that values diversity, equity, and inclusion issues.
What is equity?
Value is utilized as capital raised by an organization, which is then used to buy resources, put resources into ventures, and asset tasks. A firm commonly can raise capital by giving obligation (as a credit or through bonds) or value (by selling stock). In finance, value is responsibility for that might have obligations or different liabilities joined to them. Value is estimated for the purpose of bookkeeping by taking away liabilities from the worth of the resources. For instance, on the off chance that somebody possesses a vehicle worth $24,000 and owes $10,000 on the credit used to purchase the vehicle, the distinction of $14,000 is value. Value can apply to a solitary resource, like a vehicle or house, or to a whole business. A business that requirements to fire up or grow its tasks can offer its value to raise cash that doesn't need to be reimbursed on a set timetable.
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The distance from the sun to mercury is approximately 36,270,000 miles. the distance from the sun to saturn is 8 x 108miles. about how many times larger is the distance from the sun to saturn than the distance from the sun to mercury? about 20 times about 20 times about 4.5 times
If the distance from the sun to mercury is 36270000 miles and the distance from sun to Saturn is 8×[tex]10^{8}[/tex] miles, then it is about 22 times larger is the distance from the sun to Saturn than the distance from the sun to mercury
Given,
The distance from the sun to mercury = 36270000 miles
The distance from the sun to Saturn = 8×[tex]10^{8}[/tex] miles
Then,
The number of times larger is the distance from the sun to Saturn than the distance from the sun to mercury
[tex]\frac{8*10^{8} }{36270000} =22.05[/tex]
≈22 times
Hence, if the distance from the sun to mercury is 36270000 miles and the distance from sun to Saturn is 8×[tex]10^{8}[/tex] miles, then it is about 22 times larger is the distance from the sun to Saturn than the distance from the sun to mercury
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Find each power
-3^2 =
( - 3)^2 =
Answer:
-3^2 = -9
(-3)^2 = 9
Step-by-step explanation:
-3^2 only the 3 is being squared. So he answer is -(3) which is -3
In the second problem (-3)^2 Everything inside the parentheses is being squared. (-3)(-3) = 9
Mr. Anderson said, "Five less than one fourth of my age is 12." How old is Mr.
Anderson?
Answer:
Hes 3
Step-by-step explanation:
its 1/4 of 12 = 3
Answer:
43.
Step-by-step explanation:
12 • 4 - 5 = 43. Mr Anderson is 43.
Use the diagram to answer the questions.
*Will give brainliest*
6: Which angle forms a vertical pair with
A:
B:
C:
D:
7: Which type of angle pair are
A: Adjacent angles
B: Linear pair
C: Complimentary angles
D: Vertical angles
8: Which angle is supplementary to
A:
B:
C:
D:
Answer:
opcation a
Step-by-step explanation:
Simplify 2p-9=3(2p-5)
Answer: It is 3/2 = p
Step-by-step explanation:
1. 2p - 9 = 3(2p - 5)
2. 2p - 9 = 6p - 15
3. -9 = 4p -15
4. 6 = 4p
5. 3 = 2p
6. 3/2 = p
Answer:
6/4 or 3/2
Step-by-step explanation:
To this problem, we need to use the distributive property, and we also need to combine like terms.
2p-9=3(2p-5)
2p-9=6p-15
Subtract 2p on both sides
-9=4p-15
Add 15 on both sides
6=4p
Now divide 4 on both sides
6/4 or 3/2
I hope this helped!
Have a wonderful day!
:D
PLEASE HELP!!
A movie theater runs two group promotions. Deal A charges a $9 admission fee per person plus $15 for unlimited popcorn for the group. Deal B charges a $6 admission fee per person plus $3 for unlimited popcorn per person.
How many people must be in a group for both promotions to cost the same amount?
The number of people that must be in the group is 15.
How many people must be in the group?The expression for the total cost of Deal A is: $9p + $15
The expression for the total cost of Deal B is: $6p + $3p
Where p is the number of people in the group
When both promotions cost the same, both expressions would be equal:
$9p + $15 = $6p + $3p
In order to determine the value of p, take the following steps:
Combine similar terms
$6p + 3p - 9p = 15
p = 15
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Please solve this simple order of operations question. Make sure to show your work. No links are allowed and answers with links will be reported! First person to answer will get brainliest ! Thank you.
[5−2² + (−3)]³ ÷ (-4)
Answer:
2
Step-by-step explanation:
First you do the 2² which is 4 then 5-4 is 1-3 is -2³ is -8/-4 is 2
Pre-Calculus question
The Interpret (N · T)(t) is [tex]N[T(t)] = 20t^{2}+92t+205.[/tex]
The number of bacteria after 5 hours will be 1165.
It will take for the bacteria count to reach 2221.
As per the question statement, the number of bacteria "N" in a refrigerated food is given by [N(T) = (5T² - 4T +100)], where "T" is the temperature of the food in degrees Celsius,
And when the food is removed from the refrigerator, the temperature of the food is given by [T(t) = (2t+5)].
First we are required to find out (N · T)(t), which is N[T(t)] which can be expressed as
[tex]N[T(t)] = 5[T(t)]^{2} - 4T +100\\or, N[T(t)] = 5(2t+5)^{2} -4(2t+5)+100\\or, N[T(t)] = 5(4t^{2}+25+20t)-8t-20+100\\ or, N[T(t)] = 20t^{2} +125+100t-8t+80\\ or, N[T(t)] = 20t^{2}+92t+205.[/tex]
Then, the number of bacteria after 5 hours will be N[T(5)], i.e.,
[tex]N[T(5)] = 20(5^{2})+(92*5)+205\\or, N[T(5)] = (20*25)+460+205\\or, N[T(5)] = 500+665\\or, N[T(5)]=1165[/tex]
And finally, the time required for the bacteria count to reach 2221 can be calculated by solving the quadratic equation [tex][2221 = 20t^{2}+92t+205][/tex], i.e.,
[tex][20t^{2}+92t+205 = 2221]\\or, 20t^{2}+92t+(205-2221)=0\\or,20t^{2}+92t-2016=0\\or, 5t^{2}+23t+504=0[/tex]
And the formula to calculate the solutions of a standard quadratic equation [ax² + bx +c = 0] goes as
[tex]x=\frac{-b+\sqrt{(b^{2}-4ac) } }{2a}, \frac{-b-\sqrt{(b^{2}-4ac) } }{2a}[/tex]
Comparing [ax² + bx +c = 0] with [5t² + 23t + 504=0], we get
(a = 5), (b = 23) and (c = -504), and using these values in the above mentioned formula to calculate the solutions of quadratic equations, we get, [t = 8, (-12.6)].
Since time (t) cannot be negative, thus [t ≠ (-12.6)].
Hence, (t = 8) or, the time required for the bacteria count to reach 2221 is 8 hours.
Quadratic Equation: In algebra, any polynomial equation whose highest degree is two and can be rearranged to the standard form of [ax² + bx + c = 0], where (a ≠ 0), is known as a quadratic equation.To learn about Quadratic Equations, click on the link below.
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5
Use the drawing tools to graph the solution to this system of inequalities on the coordinate plane.
y> 2x + 4
x+y≤6
Drawing Tools
Select
Line
Dashed Line
Shaded Region
Click on a tool to begin drawing.
10-
8-
6-
4
Delete
Undo
Reset
The solution region for the given pair of inequalities is found to be the common shaded region in the graph attached.
For drawing the graph of any inequality, we first have to assume the inequality as an equation and draw the graph of the resulting equation. Hence, finding the points for the inequality , we let the inequality as:
Putting y=0, we get:
The point will be: (-2,0)
Now, putting x=0, we get:
The point will be: (0,4)
Now as the sign of inequality is >, the line of graph will be dotted.
Taking a test point (0,0) to find the shaded region, substituting this in the inequality,
So, the shaded region will be away from the test point.
Similarly, finding the points for the inequality , we let the inequality as:
Putting y=0, we get:
The point will be: (6,0)
Now, putting x=0, we get:
The point will be: (0,6)
Now, as the sign of inequality is of , the line of graph will be solid.
Taking a test point (0,0) to find the shaded region, substituting this in the inequality,
So, the shaded region will be towards the test point.
The resulting graph is attached after the solution.
The solution to the pair of given inequalities will be the shaded region that is common between both the individual inequality's shaded regions.
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The temperature dropped 12 degrees every hour for 4 hours before a blizzard started. How much did the temperature change?
Answer:
48 or -48
Step-by-step explanation:
Given that line k bisects BD at point C and that BC=9x−13 and BD=118, find CD.
Applying the definition of a segment bisector, the length of CD is: 59 units.
What is a Segment Bisector?A line segment that bisects a line segment is known as a segment bisector. It divides the line segment into two smaller segments that are equal in length to each other.
Since line k bisects BD at point C, therefore, based on the definition of a segment bisector, we have the following equation:
2(BC) = BD
BC = 9x - 13
BD = 118
Substitute the values
2(9x - 13) = 118
18x - 26 = 118
18x = 118 + 26
18x = 144
18x/18 = 144/18
x = 8
CD = BC = 9x - 13
CD = 9x - 13 = 9(8) - 13
CD = 59 units
Therefore, applying the definition of a segment bisector, the length of CD is: 59 units.
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In 2006, the population of a town was 18,310 and growing by 58 people per year. Find a formula for P, the town’s population, in terms of t, the number of years since 2006.
9b (b+3) -6 when b=2
12y +4 when y= 6
6r -3 when r=10
please help out w those 3 questions
Answer:
84, 76 , 57
Step-by-step explanation:
substitute b = 2 into the expression
9(2)(2 + 3) - 6 = 18(5) - 6 = 90 - 6 = 84
substitute y = 6 into the expression
12(6) + 4 = 72 + 4 = 76
substitute r = 10 into the expression
6(10) - 3 = 60 - 3 = 57
Answer: 84, 76, 57
Step-by-step explanation:
1. 9b (b+3) -6 b=2
9(2) (2+3) -6
18 (2+3) -6
18 (5) -6
90 -6
84
2. 12y + 4 y=6
12(6) + 4
72 + 4
76
3. 6r - 3 r=10
6(10) - 3
60 - 3
57
Find the moment of inertia about the x-axis of a thin plate with density bounded by the circle . then use your result to find =5
The lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].
What is a moment of inertia?The tendency of a body to withstand an object's angular acceleration is known as its moment of inertia. Inertia can be calculated by multiplying the mass by the orthogonal distance.Given:
Density - [tex]\delta=d(x, y)=5[/tex]Circle - [tex]x^2+y^2=16[/tex]Find the moment of inertia [tex]I_y[/tex] and [tex]I_0[/tex].
The lamina's moment of inertia about the x-axis is:
[tex]I_x=\iint_D y^2 d(x, y) d A[/tex]In the above equation, substitute the given value:
[tex]I_x=\iint_D 5 y^2 d A[/tex]Make use of polar coordinates:
[tex]\begin{aligned}x &=r \cos \theta \\y &=r \sin \theta \\d A &=d x d y=r d r d \theta \\D &=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]
As we all know, the general equation of a circle is:
[tex]x^2+y^2=r^2[/tex]The given circle equation is:
[tex]x^2+y^2=4^2[/tex]As a result, r ranges from 0 to 4.
And ranges from 0 to 2[tex]\pi[/tex].
As a result, the integral is shown below; simply enter all of the values and then integrate.
[tex]\begin{aligned}&I_x=\iint_D 5 y^2 d A \\&I_x=\int_0^{2 \pi} \int_0^4 5(r \sin \theta)^2 r d r d \theta \\&I_x=\int_0^{2 \pi} \int_0^4 5 r^3 \sin ^2 \theta d r d \theta \\&I_x=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi} \sin ^2 \theta d \theta \\&I_x=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_x=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_x=320\left(\frac{2 \pi}{2}\right) \\&I_x=320 \pi\end{aligned}[/tex]
Now, calculate [tex]I_y[/tex] and [tex]I_0[/tex].
Make use of polar coordinates.
[tex]\begin{aligned}&x=r \cos \theta \\&y=r \sin \theta \\&d A=d x d y=r d r d \theta \\&D=\{(r, \theta) \mid 0 \leq r \leq 4,0 \leq \theta \leq 2 \pi\}\end{aligned}[/tex]
As we all know, the general equation of a circle is:
[tex]x^2+y^2=r^2[/tex]The given circle equation is:
[tex]x^2+y^2=4^2[/tex]As a result, r ranges from 0 to 4.
And ranges from 0 to 2[tex]\pi[/tex].
As a result, the integral is shown below; simply enter all of the values and then integrate.
[tex]\begin{aligned}&I_y=\iint_D 5 x^2 d A \\&I_y=\int_0^{2 \pi} \int_0^4 5(r \cos \theta)^2 r d r d \theta \\&I_y=\int_0^{2 \pi} \int_0^4 5 r^3 \cos ^2 \theta d r d \theta \\&I_y=5 \int_0^{2 \pi}\left(\frac{r^4}{4}\right)_0^4 \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi} \cos ^2 \theta d \theta \\&I_y=320 \int_0^{2 \pi}\left(\frac{1-\cos 2 \theta}{2}\right) d \theta \\&I_y=320\left(\theta-\frac{\sin 2 \theta}{2}\right)_0^{2 \pi} \\&I_y=320\left(\frac{2 \pi}{2}\right) \\&I_y=320 \pi\end{aligned}[/tex]
The lamina's moment of inertia about the origin is given by:
[tex]\begin{aligned}&I_0=\iint_D\left(x^2+y^2\right) d(x, y) d A \\&I_0=\iint_D 5 r^2 r d r d \theta \\&I_0=5 \int_0^{2 \pi} \int_0^4\left(\frac{r^4}{4}\right)_0^4 d \theta \\&I_0=320 \int_0^{2 \pi} d \theta \\&I_0=320(\theta)_0^{2 \pi} \\&I_0=640 \pi\end{aligned}[/tex]
So, the moment of inertia is [tex]I_x=320 \pi[/tex].
The worth of, [tex]I_y=320 \pi[/tex].
Therefore, the lamina's moment of inertia about the origin is given by, [tex]I_0=640 \pi[/tex].
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The correct question is given below:
Find the moment of inertia about the x-axis of a thin plate with density δ=5 bounded by the circle x2+y2=16. Then use your result to find Iy and Io.
pls help me out with this geometry question
Answer:
Question 7: 20° and 160°, Question 8: 10° and 80°
Step-by-step explanation:
Complementary angles add to 90° and supplementary angles add to 180°.
Which of the following could be a real-world description of 4x − 17?
$17 in addition to the cost of 4 hot dog combos
The cost of 17 people splitting 4 hot dog combos
$17 less than the cost of 4 hot dog combos
The cost of hot dog combos less a $17 coupon split by 4 people
The answer choice which could represent the real-world description of 4x - 17 is; $17 less than the cost of 4 hot dog combos.
What could be a real-world description of the expression?It follows from the task content that the real-world description of the expression; 4x -17 is to be identified.
On this note, if the cost of 1 hot dog is; x.
Hence, the cost of 4 hot dogs is; 4x.
Ultimately, the given expression represents; $17 less than the cost of 4 hot dog combos.
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Answer: C
Step-by-step explanation:
Your mother gave you $15.80 with which
to buy a present. This covered of the
2
3
cost. How much did the present cost?
Answer: it cost 14 dollars
Step-by-step explanation:
Find the missing fraction.
5/6 - = 1/2
Answer:
Hope this helps :)
Missing fraction is 2/6
5/6 - 2/6 = 3/6 = 1/2 (simplified)
The table shows the results of an experiment in which three coins were tossed.
What is the experimental probability that at least two of the coins will be heads? The theoretical probability?
The experimental probability that at least two heads would be gotten is 11 / 25.
The theoretical probability that at least two heads would be gotten is 1/2.
What are the probabilities?Probability calculates the odds that a random event would happen. The probability the event occurs is 1 and the probability that the event does not occur is 0.
Experimental probability is based on the result of an experiment that has been carried out multiples times.
Experimental probability = number of times at least two heads would be gotten / total number of tosses
( 5 + 6 + 6 + 5)/50 = 22/50 = 11 / 25
Theoretical probability = number of times at least two heads would be gotten / total number of possible outcomes
4 / 8 = 1/2
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−6(6p−9)−10p please respond quick this is Simplify Expressions with Distribution
Answer:
[tex]-46p+54[/tex]
Step-by-step explanation:
First, distribute -6 to both 6p and -9. That gives you -36p + 54-10p
Add like terms:
-46p+54
Lamar planted 56 flowers in his garden. the ratio of orange to yellow flowers planted was 25. lamar planted yellow flowers.
From the given ratio, the number of yellow flowers are; 40 flowers
How to find the ratio?
We are given;
Total number of flowers in the garden = 56
Ratio of orange to yellow flowers is; 2:5
Thus;
Fraction of total gives;
Fraction that is orange flowers = 2/7
Fraction that is yellow flowers = 5/7
Thus;
Number of yellow flowers = (5/7) * 56
Number of yellow flowers = 40 yellow flowers
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Is the following conditional true?
If a number is a square root of an integer, then it is irrational.
Answer:
Step-by-step explanation:
The square root of an integer is either an irrational number or an integer. The latter is the case if and only if there is an integer which, when multiplied by itself, or squared, yields the number inside the symbol (the radicand) as the product. All square roots except perfect squares are irrational numbers. 3 is not a perfect square.